New cold and hot feed to a new bathroom

I am having a new bathroom put in and I am trying to figure out the supply line lay out. The bathroom will have a shower stall, toilet and sink. Water suppy will be from the cellar to the second floor. There is only room for a couple Pex lines up the the bathroom maybe more. I was thinking about running a hot and cold pex line up then manifold/tees/??? to the fixtures. Not sure what size PEX to use 1/2 or 3/4 or if I need seperate PEX feeds from a manifold in the cellar. That would be difficult but I might be able to figure out a way. My thought was to (and I am a rookie at best) Run a 3/4 cold up to feed all 3 fixtures and run a single 1/2 hot up to feed the shower and sink (less volume to exchange to get hot water to the shower).

If you have a large tub, or plan for multiple shower heads, or someone may be using the sink while you're in the shower, use 3/4" for the hot as well up into the room, and consider running 3/4" to the tub/shower, then convert to 1/2" at the valve (unless you buy a 3/4" valve!). The sink could probably get away with even 3/8", but to fill a tub, more is better. Keep in mind that the internal volume of a pipe is Pi*r^2 - the squared factor means that a little difference in r means a BIG difference in cross-sectional area and the pipe's ability to flow with minimal losses and greater volume. If it were only a single shower, 1/2" pex would likely be fine. Pex is smaller ID than copper, so 3/4" pex is only nominally larger than 1/2" copper. The fewer fittings and smoother curves of pex allows it to flow with less restrictions, but that is only part of the equation.